A377794 a(n) is the greatest number of prime factors with multiplicity of squarefree composite k such that k has lpf(k) = prime(n) such that m <= a(n), where lpf = A020639, m = floor(log k / log lpf(k)).
2, 2, 3, 3, 5, 5, 6, 6, 7, 8, 8, 9, 10, 10, 10, 11, 12, 12, 13, 13, 12, 13, 13, 14, 15, 15, 15, 15, 14, 14, 17, 17, 18, 17, 19, 18, 19, 19, 19, 20, 20, 20, 21, 21, 20, 20, 22, 23, 23, 23, 23, 23, 22, 23, 24, 24, 24, 24, 24, 24, 23, 24, 26, 26, 26, 25, 27, 28, 29
Offset: 1
Examples
Table relating the first 12 terms with prime decomposition of smallest k in A377713 (or A377792) such that lpf(k) = prime(n) and Omega(k) = a(n): n k prime factors of k a(n) ----------------------------------------------------------------------- 1 6 2 * 3 2 2 15 3 * 5 2 3 385 5 * 7 * 11 3 4 1001 7 * 11 * 13 3 5 1062347 11 * 13 * 17 * 19 * 23 5 6 2800733 13 * 17 * 19 * 23 * 29 5 7 247110827 17 * 19 * 23 * 29 * 31 * 37 6 8 595973171 19 * 23 * 29 * 31 * 37 * 41 6 9 63392725189 23 * 29 * 31 * 37 * 41 * 43 * 47 7 10 8618654420261 29 * 31 * 37 * 41 * 43 * 47 * 53 * 59 8 11 18128893780549 31 * 37 * 41 * 43 * 47 * 53 * 59 * 61 8 12 2781907990776503 37 * 41 * 43 * 47 * 53 * 59 * 61 * 67 * 71 9
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..10000
- Michael De Vlieger, Log log scatterplot of a(n), n = 1..16384.
Programs
-
Mathematica
Table[j = 1; While[Times @@ Prime[Range[i + 1, i + j]] < Prime[i]^(j + 1), j++]; j, {i, 120}]
Comments